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WMAP7 constraints on scalar-field power-law cosmology

In this paper, power-law cosmology whose scale factor is a power of time, $a \propto t^{\a}$, is investigated. Considering late universe with canonical scalar field and dust domination, we use observational data from Cosmic Microwave Background (WMAP7), Baryon Acoustic Oscillations (BAO) and observational Hubble data to find power exponent $\a$ of the power-law and other cosmological variables. The power $\a$ is found to be $0.99 \pm 0.02$ (WMAP7+BAO+$H_0$) and $0.99 \pm 0.04$ (WMAP7). These values do not exclude possibility of acceleration at 1$σ$ hence giving viability to power-law cosmology in general. When considering scenario of canonical scalar field dark energy with power-law expansion, we derive scalar field potential, exact solution, equation of state parameter and plots their evolutions using observational data. We confirm that the scenario of power-law cosmology containing dynamical canonical scalar field is ruled out by WMAP7 data since its present value of equation of state parameter does not match the WMAP7 result, i.e. the scalar-field power-law cosmology using WMAP7 gives $w_{ϕ, 0} = -0.4493 \pm 0.0300 $ while the $w_ϕ$CDM with WMAP7 data allows a maximum (+1$σ$) value of the equation of state parameter at $w_{ϕ, 0} = -0.69$.